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Previous Year Question (PYQs)

A six-faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is




Solution

Let $P(\text{even})=p$ and $P(\text{odd})=3p$ $p+3p=1 \Rightarrow p=\dfrac14$ So $P(\text{even})=\dfrac14,\quad P(\text{odd})=\dfrac34$ Sum is even when both outcomes are even or both are odd. $P=\left(\dfrac14\right)^2+\left(\dfrac34\right)^2=\dfrac1{16}+\dfrac9{16}=\dfrac{10}{16}=\dfrac58$ Answer: $\boxed{\dfrac58}$

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